8x^2+12x+1=0

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Solution for 8x^2+12x+1=0 equation: 


Simplifying
8x2 + 12x + 1 = 0

Reorder the terms:
1 + 12x + 8x2 = 0

Solving
1 + 12x + 8x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
0.125 + 1.5x + x2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + 1.5x + -0.125 + x2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + 1.5x + x2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + 1.5x + x2 = 0 + -0.125
1.5x + x2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
1.5x + x2 = -0.125

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = -0.125 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = -0.125 + 0.5625

Combine like terms: -0.125 + 0.5625 = 0.4375
0.5625 + 1.5x + x2 = 0.4375

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 0.4375

Calculate the square root of the right side: 0.661437828

Break this problem into two subproblems by setting 
(x + 0.75) equal to 0.661437828 and -0.661437828.


Subproblem 1
x + 0.75 = 0.661437828

Simplifying
x + 0.75 = 0.661437828

Reorder the terms:
0.75 + x = 0.661437828

Solving
0.75 + x = 0.661437828

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 0.661437828 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 0.661437828 + -0.75
x = 0.661437828 + -0.75

Combine like terms: 0.661437828 + -0.75 = -0.088562172
x = -0.088562172

Simplifying
x = -0.088562172


Subproblem 2
x + 0.75 = -0.661437828

Simplifying
x + 0.75 = -0.661437828

Reorder the terms:
0.75 + x = -0.661437828

Solving
0.75 + x = -0.661437828

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -0.661437828 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -0.661437828 + -0.75
x = -0.661437828 + -0.75

Combine like terms: -0.661437828 + -0.75 = -1.411437828
x = -1.411437828

Simplifying
x = -1.411437828


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.088562172, -1.411437828}

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